It is known that the distance from the cross section of three points a, B and C on the sphere to the center O is equal to half of the radius, and ab = BC = CA = 3cm I want the most clear and easy to understand answer process

It is known that the distance from the cross section of three points a, B and C on the sphere to the center O is equal to half of the radius, and ab = BC = CA = 3cm I want the most clear and easy to understand answer process

According to the meaning of the title, a triangular pyramid o-abc is a regular triangular pyramid
Let △ ABC Center (i.e. the perpendicular foot from the spherical center O to the section ABC) on the bottom surface of a regular triangular pyramid o-abc be p, then
PA = Pb = PC, ∠ PAB = PBA = 30 degrees, the distance from P to AB is half of PA
Square of PA = (PA / 2) + (AB / 2)
Square of PA = 3 (square centimeter)
Square of PA + square of OP = square of radius
Radius r = 2 (CM)
The volume of the ball v = 4 / 3 * pie * r cube = 4 / 3 * pie * 8 = 32 / 3 * pie (CC) ≈ 33.5104 (CC)
The surface area of the ball s = 4 * pie * r square = 16 pie (square centimeter) ≈ 50.2656 (square centimeter)